Find the limit of $\frac{x^2-x-6}{x-3}$ as $x$ approaches $3$

Step-by-step Solution

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Final answer to the problem

$5$
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Step-by-step Solution

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  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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1

Factor the trinomial $x^2-x-6$ finding two numbers that multiply to form $-6$ and added form $-1$

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$\begin{matrix}\left(2\right)\left(-3\right)=-6\\ \left(2\right)+\left(-3\right)=-1\end{matrix}$

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Learn how to solve limits by factoring problems step by step online. Find the limit of (x^2-x+-6)/(x-3) as x approaches 3. Factor the trinomial x^2-x-6 finding two numbers that multiply to form -6 and added form -1. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying. Evaluate the limit \lim_{x\to3}\left(x+2\right) by replacing all occurrences of x by 3.

Final answer to the problem

$5$

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Function Plot

Plotting: $\frac{x^2-x-6}{x-3}$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Limits by Factoring

Limits that require factorization techniques to solve them.

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